The total surface area of a cuboid with length $l$, breadth $b$, and height $h$ is given by the formula: $$ TSA = 2(lb + bh + hl) $$ Given the length $l = 8$ cm, breadth $b = 3$ cm, and height $h = 4$ cm, we can substitute these values into the formula: $$ TSA = 2((8)(3) + (3)(4) + (4)(8)) $$ $$ TSA = 2(24 + 12 + 32) $$ $$ TSA = 2(68) $$ $$ TSA = 136 $$ So, the total surface area of the cuboid is 136 cm$^2$.